Bearing mounting



Sept. 5, 1944. E. F. MARTINEC BEARING MOUNTING FiledJune 16, 1942 3 Sheets-Sheet l FIG): b"

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sept. 5, 1944.v

ED PLA/VE SL/PPAGE ANGLE FROM HOR/ZONTAL E. F.` MARTINEC BEARING MOUNTING Filed June 16, 1942 5 Sheets-Sheet 3 SHURE uRoMy-ER SCALE FIG. 23.

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ArToR/VE Y Patented Sept. 5, 1944 UNITED STATES PATENT. OFFICE BEARING MOUNTING f Eugene F. Martinec, Cleveland, Ohio, assIgnor-to 4 Norma-Hoffmann Bearings Corporation, Stamford, Conn.. a cornorationof New York Application June 16, 1942, serial Noi 447,231-

2 Claims. (Ci. :tos-184)l This invention relates to bearing mountings. The object of the invention is to provide means operative in connection withball bearings whereby pitting of races is prevented, and secondly to' prevent creep, slippage or movement of bearing parts with respect to adjacent mounting mem-K.

bers.

ball bearings is the pitting of races by balls held therein. When a, ball bearing is suddenlysub:

jected to a sharp shock or to an excessivedimpactf load which translates its force to a ball bearingl in a manner not contemplated by the design. Y and structure of such a ball bearing, the entire force, or almost the entire force, is suddenly ap One of the disadvantagesattendant the use of plied at an axially inclined angle to one or more of the balls, and the race is indented or pitted. Such indenting or pitting takes place adjacent the marginal portion of thesrace, and uponthe rotation of the race, the balls-rollingfover .these pits are caused to vibrate severely, with resultant increased roughness, due to the depth of the pitting. Many attempts have been made to prevent l this pitting. Frequently, it happens that manufacturers supplying their customers, are required f to send repair or service men to their customersinthe belief that faulty ball bearings have been.

delivered, only to ndthat such bearings had` been subjected to forces causing such pitting. Attempts to solve this Vproblem to prevent such pitting caused by sharp blows have beenyunsuccessful. The annual damage loss is very great,-v

to say nothing of the loss of time awaiting repair or substitute bearings. The matter of pitting becomes especially pronounced when ball bearings are used with articles, the use or abuse of which causes the bearings to be subjected to sudden diagonal loads in the form of sharp shock applications.

It has been found that when small motors or small units are mishandled in assembly or in shipuation becomes 4greatly aggravated when` the races have been pitted.

The present invention solves this problem and provides means first to prevent such pitting, and secondly, to prevent creeping or relative m'ovement ofthe outer race in its housing, and in respect toA other mounting part-s.

The inventionl consists in the provision of resilient means interposed between the ball bearings and the application of -a diagonal force or excessive `load impact line, to enablethese means to absorb such an impact load, such means hav#- ing sumcicnt inherenty resiliency to provide a Y, safety factor reservoir over the highest expected sharp impact loadvf'or that size of hearing. Such means consist of an interposed block of rubber or synthetic rubber, of a weight, thickness and consistencyof porosity which will absorb the shockv without' reaching its elastic limit, so that a further potential of inherent resiliency remains.

That may becalled a reservoir of inherent resilicncy. l.

` The invention consists also. in providing a stationary structure which seats against the outer face of the outer-race ring and which structure has a surface contiguous to that face, so that the contiguous facesl sofinterlock, or frictionally hug, so that the stationary surface holds the `face of Y the racer ring, andthe youter race ring is prevented- 30' 'from rotation. Likewise this stationary structure has a similar face in-contact with the face of the opposite housing member so that these continguous races' likewise interlock and' are prevented mentand dropped for example, then such pitting alsoresults.`

Ordinary roller skates for example .employing ball bearinlzs ofthe generaltypes like crudely made up and cone or thrust bearings'have the disadvantage of easily. tiring; the L users, while those employing precision or low friction bearings avoid this disadvantage, but have' another disad' vantagethat anoise is produced due to' certain mounting parts sliding or vibrating, which. is sh-rill, disagreeable, and -frequently interferes with the accompanying music attendant fancy gure skating for public exhibition purposes. This sitabsorbing layer will preventpitting.v If .pitting is not likely. to arise,` theslippage preventing means may. be used.4 Or, ythey may` be used together, as hereinafter described.`

A structure embodying the. invention may be` inthe form 'of'` separate shims esting against a body olif i;uooer .which oodya surfaces or shims.

y l l as, afiresi-.rvoirjof inherent resiliency to' absrbithe shock load, or, f the latter may be provided integrally with such'` of such rubber for the inherent resiliency reaerl voirI that it still has a surplus compression factor beyond that necessary to absorb the shock load. and also the selection of such hardness as may be co-related thereto.

By rubber is intended to be included natural rubber, synthetic rubber or similar exible compressible material.

. The invention will inafter, embodiments ings, and the invention in the appended claims.

In the accompanying drawings- Fig. l is a central section of a ball bearing embodying the pitting preventing invention applied to a roller skate wheel;

Fig. la is a similar section, but diagramatically and fragmentary, to show a bearing with a pitting preventing means on both sides of the outer race ring;

Fig. 2 is a perspective fragment of` a rubber ring broken away;

Fig. 3 is a perspective fragment of the rubber ring shown in Fig. 2, but provided integrally with friction surfaces or films;

Fig. 3a is another form thereof, with the friction films separated from the body of the rubber ring: Y

Fig. 4 is a fragmentary perspective of the rubber ring of the kind shown in Fig. 1, but in its repose position (not compressed);

Fig. 4a i: a like view but with the rubber partially compressed as in the position shown in Fig. 1. but still retaining a reservoir for inherent resiliency;

Fig. 4b is a like view but with the rubber compressed beyond its power to retain a reservoir for be further describedherewill be shown in the drawwill be finally pointed out shown in Fig. l, and with the layer of rubber not compressed but fully expanded;

Fig. is a like view, showing the same layer compressed as whenin use, and showing how the layer expands into the spaces of the adjacent parts:

Fig. 11 shows a layer of rubber now of an initial configuration as shown in Fig. 10. and with separate surface films or shims having friction increasing characteristics;

Fig. 12 shows the rubber layer and illms of Fig. 11 integrally joined;

Fig. 13 shows the same structure as in Fig. 12 in duplex form for a bearing on each side thereof;

Fig. 14 shows another embodiment, in which the rubber layer is fastened to the outer race ring by grooves and ridges, and showing the same in initial or uncompressed position;

Fig. 15 shows the same embodiment as shown in Fig. l4, .but now compressed by external means applied thereto; the friction increasing surface is not shown in Figs. 14 and 15, though it may be applied to the faces of the rubber layer;

Fig. 16 shows another embodiment, engaging a cut out of the outer perimeter of outer race ring, and without friction films;

Fig. 17 shows the same embodiment provided with friction films; 4

Fig. 18 shows another embodiment with a tongue and groove connection, and without friction lms;

Fig. 19 shows the same embodiment as shown in Fig. 18, but provided with friction films;

Fig. 20 shows the embodiment of Fig. 18, with external pressure applied;

Fig. 21 is a chart showing the ratio of compression ilow under load and pressure applied for sponge rubber which would be used for light load thrust applications;

Fig. 22 shows a similar chart for a plain rubber inherent resiliency, this view being for the purpose of illustration, and none of the views shown in Figs.-4, 4a `and 4b, have `friction lms, whichy will be shown elsewhere;

Fig. 5 is a fragmentary race ring, broken away, the same;

Fig. 6 isa diagrammatic fragmentary drawing of races and a ball therebetween to show a loose relationship, to illustrate a condition wherein any shock or impact applied will readily pit the race;

Fig. 6a is a diagrammatic drawings of the same parts but showing the same in a tight relationship to illustrate that in such a condition part of the shock or impact may be absorbed;

Fig. 7 is a diagram chart to show how the sharp shock or impact load enters the ball imprinting zone when no cushioning is present.

Fig. 8 isanother diagram or chartto show that wnerecushioning is present the sharp shock or impact load does not'exceed a certain amount whereby the cushioning decreases the instantaneous load peak so that there still remains a safety factor or a reservoir of inherent resiliency before ball imprinting takes place;

Fig; 9 is a fagmentary section of an embodiment of my pit-preventing invention, such as perspective of an outer and showing pitting of which initially has a considerably greater degree of hardness than sponge rubber, the charts of Figs. 21 and 22 showing characteristics of rubber suitable to carry out the pit preventing invention;

Fig. 23 shows a chart showing the ratio of the slippage angle (coefficient of friction) with two types of surface frictional resistance films and the hardness of the rubber, this chart being for sponge rubber; and

Fig. 24 shows a chart like Fig. 23, but now for plain rubber.

Similar reference characters indicate like parts throughout the several views.

Referring to the drawings, and more particularly to Figure l, the ball bearing therein shown is applied to a roller skate wheel, of the type shown and claimed in my copending application. Ser. No. 372,156, filed December 28, 1940, now matured into Patent No. 2,304,944, issued December 15, 1942'. The outer rim I0 has a wedge shaped interiorly extending member Il, the bore I2 of which is engaged by a ring shaped housing member |3,which has at one end a ring shaped projection I4 engaging the recess I5 of the rim or roller I0. Adjacent this end but interiorly of the housing member I3, a shoulder 20 is provided. The outer end of the housing member I3 has an interior screw-threaded portion I6, adapted to be engaged by an exterior screw-threaded portion l1 of a nut member I8. An anti-friction bearing consisting of an outer race ring 2|, an inner race ring 22, balls 23, a bail-bearingcage 24 and dust seals 25, has its outer'race ring disposed against the shoulder 2l, and is held against the shoulder by the nut member I8, through the instrumentaliity of a rubber washer 25. Which Will be hereinafter described more .in detail. (The innerrace ring 22 is secured to a shaft 21 shown in dotted 1ines,fby the inner race ring seating atone side, against a shoulder 28 of the shaft and by a nut 29 having an interior thread (not shown) engaging an exterior thread (not shown) at the.

end of the shaft 21, the nut pressing against the free end ofthe inner race ring when properly applied.

. slightly further compressed and st ill retain a resA Thevrubber washer 26 has one surface facing and contacting with the outer planular surface of the outer-'race ring 2|, and another surface parallel therewith contacting with the planular surface of the contiguous nut member I8.

The third surface of the rubber washer or layer is the perimeter surface and this is spaced from the inner circumferential surface of the housing member I3 to allow for the ow of the rubber if pressed to a. still greater degree than shown in Fig. 1 and until it will press against this housing bore. l

The fourth and radially innermost circumferential surface of the washer is freeand may flow inwardly if further pressure be applied. In this particular embodiment, shown in Fig. 1 that sur- Flg. '7. To carry out the invention it is necessary to retain a certain amount of inherent resiliency, and this certain amount maybe referred to as a reservoir of inherent resiliency. While the shape of the layer shown in Figs. l, 2 and 4a, may be ervoir of inherent resiliency, it must not'be compressed to the degree shown in Fig. 4b. 'I'he description Just made relates' to the characteristic of th'e layerbinsofar as inherent resiliency is concerned. I y

In orderl to clearly demonstrate the relationship of the cushioning effect oi' the rubber washface of the rubber layer or washer which conj tacts with the outer race ring extends beyond the outer race ring inwardly toward the shaft and' is free of any contacting or opposing surface.

'I'he foregoing structure and description is part of the aforesaidapplication, Ser. No. 372,156, filed December 28, 1940, and the action thereof with further improvements thereon will now be described.

The rubber layer 26 of Fig. 1 is shown in Fig. 2, and inthe formshown in Fig. `2 it corresponds to that shown in Fig. 1, namely, it is under partial compression; the part 30 is the surface which contacts with the bearing outer ring, the surface 32 is the perimeter surface, the surface 33 is that surface which contacts with the4 contiguous surface'of the nut member, and the surface 34 is the inward circumferential surface. The rubber as shown in Figs. 1 and 2 is so arranged and so act- `ed upon by the pressure applied between the outer race ring 2| and the nut/.member I8 that it is not entirely compressed. It still has an iner necessitating a reservoir for further inherent resiliency, the charts shownin Figs. 7 and 8 show as the abscissa the time interval and the ordinate the shock load. In such cases where a ball bearing has no cushioning layer, as in Fig. 7, the curve rises sharply to the point corresponding to the greatest/shock force in the almost instantaneous time interval, and then descends. l 'I'his Fig. 7 curvel is based upon actual tests. The ball imprintingzone is defined by the limits of the f greatest sharp shock force asindicated by horizontal line 92 down to a lower shock load indicated by the horlznntal line 9| at the lower end of the double pointed arrow 90. It will therefore be seen from an examination of this curve that that the shock load is absorbed-in the time inv herent resiliency enabling it to be further com. I

pressed. It is however, not advisable to further compress it excepting only very slightly so that it retains the nature of a safety factor or a reservoir against unusual or unexpected or excessive sharp shock pressures.

Inv Fig. 4, the layerv26 is shown in its initial or expanded form; in Fig. 4a pressure has been applied as indicated by the arrow 35, and the washer has been partiallycompressedl and radially lengthened. The 'shape of the Washer shown `in Fig. 4a is exactly the shape of the washer shown in Figs. 1 and 2. In Fig. 4b the washer has been still further compressed due to the action of the forces indicated by the arrow 36, and this state-of compression is assumed as beyond the capacity of the rubber for any further inherent resiliency and is shown in order to illustrate that a fully compressed layer should not be usedin the car-t rying out of this invention,y since such a fully A`compressed layer does -not have any further in-l herent resiliency, or any reservoir or lany safety factor, and in consequencecannot'be Aapplied for the purpose of carrying out this invention. The` use 'of such a highly compressed layer would bring about a pitting of the race in the manner shown in Figure 5 under the operation shown in where there is no cushioning effect the race of a ball bearing will be ball imprinted when the sharp shock load force exceeds a certain amount. In Fig. 8 however, is shown a relationship where a cushioning layer is applied Iand it will be noted terval provided by cushioning to such an extent that its force does not reach the lower range corresponding to imprinting, namely the horizontal line 9|. As the curve does not extend to the lower limit of the ball imprinting zone, there is still left a reservoir of inherent resiliency to take care of shock loads greater than the average intended to be assumedJby the particular rubber layer or washer placed between an outer race or an inner race of a ball bearing, and some restraining member' of the rubber layer.

y l.zone for compound, depending of course upon the effective area and thickness of the rubber being compressed. It will be-noted that the curve rises steeply after its straight line portion indicating that its reserve reservoir of resiliency is almost used up. Another piece of sponge rubber would have slightly different results depending upon its particular compounding, but in general I similar thereto.

In Fig. 2 2 is shown a chart fora plain rubber (not sponge rubber) compound of considerably greater degree of r*hardness than the aforesaid sponge rubber. The range here is from about ,l1/2 pounds total pressure and .002 inch compression ow, to about 10 pounds total pressure and .009 inch compression flow as indicated by -Eifective compression .zone for compound. 4Again the curve rises sharply after its straight test, so

line portion, indicating again that its reserve reservoir of resiliency is almost used up.

Fig. 23 is a chart showing the relation of the slippage angle (or coeiiicient of friction) with the hardness of sponge rubber with a nlm. s There are shown two different' types of surface for the rubber, one, the upper one using a Celiophane surface on the mold used to provide the rubber, and the other. or vlower one using a parchment surface on the mold used to produce l the rubber, the former providing the smoother surface of the rubber.

In Fig. 24 similar charts are shown, one, the. upper, forthe Cellophane surface, and one, the\ lower, for the parchment surface, both for plain (not sponge) rubber. From the curves of Figs.

23 and 24, it is seen, that with the same film finish the harder the background the more the slippage in terms of a lower inclined angle in that to get the'best slippage factor of a 20 certain finish it is vbest to have a softer backing to the finish. Charts in Figs. 23 and 24 are based on the incline plane friction tests of A. S.

T. M. Again, in selecting the layer with a holding o-r friction force, such rubber should be se- 25 lected within the range given by the charts of Figs. 23 and 24. When selecting reservoir` layer, rubber charts similar to those of Figs. 21 and 22 should be followed. And when these two features or inventions are joined al1 charts must be 3o taken into consideration.

In Figs. 9 to 20, I have shown various embodiments of my invention utilizing the foregoing principles.

In Fig. 9, a rubber layer generally like that of Fig. 1, is shown. With a suitable further compression force, this washer is converted to the shape shown in Fig. l0,in which the upper end of the washer viewed in respect to Fig. 10 is shaped to enter the curved recess (Figure 9) 40 and to take a shape as shown by 5I in Fig. 10. Likewise the rubber layer will exude between the nut and the housing as shown by the portion 52 as shown in Fig. 10. Both of these portions 5l and 52 extend circumferentially around the out- 45 er race and the enclosing nut, providing extra large area of gripping power aided by the wedging effect at the corner of the bearing ring and at the corner of the nut. Furthermore. the rubber exudes to form alprotuberance of rounded 50 shape as indicated at l53 in Fig. 10. Figs. 9 and 10 can be viewed as having friction skin surfaces on the rubber layer facing'the outer race ring and facing ,the nut face respectively or viewed merely as a rubber layer without such friction 55 skin surfaces and intended to be used merely to absorb shock without the additional attribute of frictlonally holding the outer race ring from rotating. In Fig. 11, I have shown a, rubber layer ring or layer shaped to correspond to the final ,o shape shown in Fig. 10, and this layer' 55 has a curved por-tion 58, a ridge portion 51, al1 like that shown in Fig. l0, andto this layer 55, shims 58 of friction producing substance may be applied and made part thereof by vulcanization or 5 otherwise, cr as before stated, the layer l5 may. be immediately provided in the course of its manufacture with skin friction surfaces analogous' to the shims 58. The joinder of the rubber washer 55 and the shims 58 integrally connected, is shown in Fig. 12 with the layer 55a and friction or shim surfaces 58a. Iflt is desired to have a structure such as Fig. 12. but in such form for use with two bearings or two outer race rings, the duplex form of washer b has friction sui'-r .u

faces IIb. I'hestructures shown in Figs. 12l and 13 are the initial structures having such attributes as to be capable of being pressed with a reservoir remaining, but not intended to be compressed beyond that point.

In Fig. 14, the outer race ring has an interior series of grooves 60 and the rubber layer is lshaped to have a series of ridges on the arm Il and at the same time to have an inclined surface 32 abutting against Athe 'inclined surface 63 of the outer race ring. In this case, the rubber layer may be snapped into position and used or supplied with the outer race ring, that is, with the entire ball bearing. When pressure is applied to a layer/of this type by a force 68 on a member 63a, it then provides the extensions il and 66 of the rubber and an inner rounded contour 6l as shown` in Fig. 15. The exterior face of ,the rubber layer, which face abuts against the face of the member 68a may be provided with a friction film.4

Another form consists in providing a cutout to form a shoulder 10 and to have the rubber layer of inverted L-shape as shown in Fig. 16. When pressed, the layer forms a. circular contour shown in dotted lines. This type is shown in Fig. 16 and if it be desired to provide skin surfaces, such a form is shown in Fig. 17, the skin or film surfaces being indicated by 12. The outer race ring might be provided in its outer planular surface with a groove recess 14 and the rubber layer 15 provided with a tongue projection 'i6 to enter said recess, and if it be desired to provide skin surfaces, vthese are indicatedl in Fig. 19 by 11. When a structure such as shown in Fig. 18 is subjected to pressure indicated by the arrow 18 in Fig. 20, the circular contour 'I9 and 80 are thereby formed.

The importance of the relationships just described will be recognized from the fact that ball bearings of the type described when applied to devices such as skating wheels very frequently are subjected to extreme shocks or diagonal forces such as indicated by the arrow 31 in Figs. 1 and 6a. In such cases, the entire diagonal pressure may be translated to one or two of the balls of the ball bearing, and thereby the balls are forced into therace of the race ring whereby a pitting or indentation results. When such pitting takes place near the edge of the race the resultant vibration may bring about an enlargement of the pits or indentations. Races of ball bearings very frequently present a pitting action such as shown in Fig. 5, in which 39 indicates the average form of pit resulting from the ball impressing itself into the race.

Another reason for pitting is a condition where the races are too loosely spaced with respect to the balls as in Fig. 6. Assuming the upper race in Fig. 6 be subjected to a quick downward or axial movement, then it will move downwardly or laterally and transpose its force to the bali, and the ball will transpose its so acquired force to the lower race ring and its race. This rapid action will indent the race as shown in Fig. 5. If however, this same shock force be applied to a ball and race relationship as shown in Figi 6a, wherein the races form a relative tight fit with the ball, then that same shock force will receive a certain amount of distribution and be more evenly distributed in the parts, andthe intensity of the force upon the lower race will be somewhat less than that of Fig. 6. 'I'he improved reservoir layer and the friction film however absorb the shock and impact forces, irrespective of the Anot sufficiently close to act upon each other in a binding manner, and consequently there is a slippage or relative movement between the outer race ring and the housing member, causing wear, increasing looseness and noise. This is particularly so since in the embodiment shownl in Fig. 1, the outer race ring continually rotates in contrast to the more general use of an anti-friction ball bearing in which the outer race ring is stationary and the inner race ring rotates. In the embodiment shown in Fig. 1, the inner race ring is stationary as it is secured in the manner before described, to the stationary roller skate shaft 21.

In order to prevent this slippage, the rubber layer or washer 26 is provided at its surfaces 30 and 33 with skin surfaces of a character to eXert the largest possible friction between such skin surfaces and the outer surface of the outer race ring and inner face' of the nut respectively. It is known in physics that where two very highly polished surfaces are placed in contact with each other, the planular relationship is such that al1 air is excluded and thereby the two contacting surfaces adhere to each other in such a manner that it is difficult, if not impossible, to move one surface in respect to the other. vThis physical phenomenon is availed of by providing the surface 30 of the rubber washer for example with such a. planular relationship that it coacts with the planular relationship of the outer face of the outer race ring in such a manner that the outer race ring, is, so to say, keyedv to the rubber washer 2B. These skin surfaces 31a. may be made integral with the rubber washer 26 as shown in Fig.

`The conjoint action of both of these inventions is such that slippage of the race ring in its housing is prevented, and that shock loads are absorbed, whereby pitting is prevented.

Wherever rubber is spoken of it is intended that there be included therein a synthetic rubber or a compound of rubber, or any other material having substantially the same vibration and force absorbing factor, inherent resiliency and friction creating characteristics.

I have described several forms of my invention,-

butobviously various changes may be made in the details disclosed without departing from the spirit of the invention as set out in the following claims.

What I claim is:

1. In'a bearing mounting `for a cylindrically bored housing having internal shoulders with opi positely disposed parallel faces relatively movable towards each other, an outer race ring having lateral faces and a cylindrical external contour slidably seated in the bore of the housing between said parallel faces of the shoulders, and a rubber ring .interposed between one of the shoulder faces and one of the race ring faces, the sides of the rubber ring being contiguous to said faces. the combination of means for partially compressing the rubber ring between the contiguous race ring face and contiguous shoulder face 3', or may be made in the form of separate shims such as shown in Fig. 3a in which latter figure the rubber washer 26 and the skin surface shims 34a are spaced from one another.v These shims with thin skin surfaces are preferably combined with the body portion-of the rubber washer asshown in Fig. 3, or if desired, Figs. 4, 4a and 4b may be considered as having such skin surfaces.

The criterion as to the shock absorbing layer is that after the maximum shock force towhich the use of the bearing is expected to be subjected has been determined, about a third of the thickness of the absorption depth is added to act as a reservoir for unexpected forces. From the boundary of the'invention it is sufficient if there be some depth beyond the normal maximum absorption depth, so that most Aif not all of the shock forces be absorbed instead of being transmitted to the bearing. The criterion as to the friction causing film is that it has the character of its surface so related to the character of the contiguous surfaces that no relative movement of these surfaces can take place. The character of these surfaces can be ascertained and prede-l termined by tests and by tables formed from prior tests.

to absorb the axial component 4of any diagonal shock load to which the mounting is subjected, means for locking the face of the shoulder to the contiguous side face of the rubber ring preventing relative movement therebetween when the ring is partially compressed, and means on the face of the rubber ring contiguous tp the race ring face having a relatively high coefficient of friction preventing rotation of the race ring with respect to the rubber ring, whereby the rotation of the race ring in respect to the housing is prevented.

2. In a bearing mounting for a cylindrically bored housing having internal shoulders with oppositely disposed parallel faces relatively movable towards each other, an outer race ring having lateral faces and a cylindrical external contour slidably seated in the bore of the housing between said parallel faces of the shoulders, and

a rubber Lring interposed between one of the shoulder faces and one of the race ring faces. the sides of the rubber ring being contiguous to said faces, the combination of means for partially compressing the rubber ring between the contiguous race ring face and contiguous shoulder face yto absorb the axial component of any diagonal shock load to which the mounting is subjected,

means for locking theface of the shoulder to the contiguous side face of the rubber ring preventy EUGENE F. MARTINEC. 

